Solve 0,25-11/5/-3frac{4{5}+1,9}+10-2,5/frac{1{2}-0,75}

$$\frac { 0,25 - 1 \frac { 1 } { 5 } } { - 3 \frac { 4 } { 5 } + 1,9 } + \frac { 10 - 2,5 } { \frac { 1 } { 2 } - 0,75 }$$

Evaluate

$$-29,5$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\frac{0,25-\frac{5+1}{5}}{-\frac{3\times 5+4}{5}+1,9}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Add 5 and 1 to get 6.

$$\frac{0,25-\frac{6}{5}}{-\frac{3\times 5+4}{5}+1,9}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Convert decimal number 0,25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{1}{4}-\frac{6}{5}}{-\frac{3\times 5+4}{5}+1,9}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{6}{5} to fractions with denominator 20.

$$\frac{\frac{5}{20}-\frac{24}{20}}{-\frac{3\times 5+4}{5}+1,9}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Since \frac{5}{20} and \frac{24}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-24}{20}}{-\frac{3\times 5+4}{5}+1,9}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Subtract 24 from 5 to get -19.

$$\frac{-\frac{19}{20}}{-\frac{3\times 5+4}{5}+1,9}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Multiply 3 and 5 to get 15.

$$\frac{-\frac{19}{20}}{-\frac{15+4}{5}+1,9}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Add 15 and 4 to get 19.

$$\frac{-\frac{19}{20}}{-\frac{19}{5}+1,9}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Convert decimal number 1,9 to fraction \frac{19}{10}.

$$\frac{-\frac{19}{20}}{-\frac{19}{5}+\frac{19}{10}}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Least common multiple of 5 and 10 is 10. Convert -\frac{19}{5} and \frac{19}{10} to fractions with denominator 10.

$$\frac{-\frac{19}{20}}{-\frac{38}{10}+\frac{19}{10}}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Since -\frac{38}{10} and \frac{19}{10} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{19}{20}}{\frac{-38+19}{10}}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Add -38 and 19 to get -19.

$$\frac{-\frac{19}{20}}{-\frac{19}{10}}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Divide -\frac{19}{20} by -\frac{19}{10} by multiplying -\frac{19}{20} by the reciprocal of -\frac{19}{10}.

$$-\frac{19}{20}\left(-\frac{10}{19}\right)+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Multiply -\frac{19}{20} times -\frac{10}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-19\left(-10\right)}{20\times 19}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Do the multiplications in the fraction \frac{-19\left(-10\right)}{20\times 19}.

$$\frac{190}{380}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Reduce the fraction \frac{190}{380} to lowest terms by extracting and canceling out 190.

$$\frac{1}{2}+\frac{10-2,5}{\frac{1}{2}-0,75}$$

Subtract 2,5 from 10 to get 7,5.

$$\frac{1}{2}+\frac{7,5}{\frac{1}{2}-0,75}$$

Convert decimal number 0,75 to fraction \frac{75}{100}. Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{1}{2}+\frac{7,5}{\frac{1}{2}-\frac{3}{4}}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{1}{2}+\frac{7,5}{\frac{2}{4}-\frac{3}{4}}$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}+\frac{7,5}{\frac{2-3}{4}}$$

Subtract 3 from 2 to get -1.

$$\frac{1}{2}+\frac{7,5}{-\frac{1}{4}}$$

Divide 7,5 by -\frac{1}{4} by multiplying 7,5 by the reciprocal of -\frac{1}{4}.

$$\frac{1}{2}+7,5\left(-4\right)$$

Multiply 7,5 and -4 to get -30.

$$\frac{1}{2}-30$$

Convert 30 to fraction \frac{60}{2}.

$$\frac{1}{2}-\frac{60}{2}$$

Since \frac{1}{2} and \frac{60}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-60}{2}$$

Subtract 60 from 1 to get -59.

$$-\frac{59}{2}$$

Factor

$$-29,5$$